A source of sound is moving along a circular orbit

Question

A source of sound is moving along a circular orbit of radius 3 meters with an angular velocity of 10 rad /s. A sound detector far away from the source is executing linear simple harmonic motion along the line BD with an amplitude BC = CD = 6 meters. The frequency of oscillation of the detector is 5/πper second. The source is at the point A when the detector is at the point B. Ifthe source emits a continuous sound wave of frequency 340 Hz, find the maximum and the minimum frequencies recorded by the detector.

Aditi Chauhan · Accepted Answer

Hello Student,Please find the answer to your questionThe angular frequency of the detector = 2&pi;v= 2&pi; x 5/&pi; = 10 rad/sThe angular frequency of the detector matches with that of the source.&rArr; When the detector is at C moving towards D, the source is at A1 moving leftwards. It is in this situation that the frequency heard is minimumv&rsquo; = v [v &ndash; v 0/v + vs] = 340 x (340 &ndash; 60)/(340 + 30) = 257.3 HzAgain when the detector is at C moving towards B, the source is at A3&shy; moving rightward. It is in this situation that the frequency heard is maximum.v&rdquo; = v[ v + v0/v &ndash; vs] = 340 x (340 + 60)/(340 &ndash; 30)= 438.7 HzThanksAditi ChauhanaskIITians Faculty

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